Adjusting vertical spacing in fractions?

You can use \cfrac, which is thought for continued fractions, which this is a case of:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
t =
\frac{\dfrac{T_1}{T_2}}{1+\dfrac{Q_1}{Q_2}}=
\cfrac{\cfrac{T_1}{T_2}}{1+\cfrac{Q_1}{Q_2}}
\end{equation*}

\end{document}

I would use inline-fraction notation rather than stack two \dfrac expressions. The presence of the / characters ensures almost automatically that the numerator and denominator terms are not placed too closely to the fraction bar.

\documentclass{article}
\usepackage{amsmath} % for "\dfrac" macro and "equation*" env.
\begin{document}
\begin{equation*}
   t=\dfrac{T_1/T_2}{1+Q_1/Q_2}
\end{equation*}
\end{document}

Use\cfrac, combined with \bigstrut for the numerator:

\documentclass{article}
\usepackage{amsmath}
\usepackage{bigstrut}

\begin{document}

\begin{equation*}
 t = \frac{\cfrac{T_1}{T_2\bigstrut[b]}}{1+\cfrac{Q_1}{Q_2}}
\end{equation*}

\end{document}